Factor Calculator

Factors of 800

The factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, and 800. In total, 800 has 18 factors. Its prime factorization is 2⁵ × 5², and the sum of all its factors is 1953.

All factors of 800

Here are all 18 factors of 800, listed from smallest to largest.

124581016202532405080100160200400800

Factor pairs of 800

These 9 pairs of whole numbers each multiply to give 800.

1 × 800 = 800
2 × 400 = 800
4 × 200 = 800
5 × 160 = 800
8 × 100 = 800
10 × 80 = 800
16 × 50 = 800
20 × 40 = 800
25 × 32 = 800

Prime factorization of 800

Dividing 800 by the smallest prime at each step gives its prime factorization:

800 ÷ 2 = 400
400 ÷ 2 = 200
200 ÷ 2 = 100
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
Result: 800 = 2 × 2 × 2 × 2 × 2 × 5 × 5 = 2⁵ × 5²

The distinct prime factors of 800 are 2, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 800

A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.

Factor tree of 80080024002200210025022555
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 800

Number of factors18
Sum of factors1953
Sum of proper factors1153
Prime factorization2⁵ × 5²
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 800 interesting

  • 800 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 9 different ways.
  • 800 is an abundant number: its proper factors sum to 1153, which is 353 more than 800 itself.

How to find the factors of 800 yourself

Divide 800 by each whole number starting from 1. Whenever the division leaves no remainder, both the divisor and the quotient are factors. You only need to test up to √800 ≈ 28.28, because every factor above that pairs with one below it.

800 ÷ 1 = 800 ✓
800 ÷ 2 = 400 ✓
800 ÷ 4 = 200 ✓
800 ÷ 5 = 160 ✓
800 ÷ 8 = 100 ✓
800 ÷ 10 = 80 ✓
800 ÷ 16 = 50 ✓
800 ÷ 20 = 40 ✓
800 ÷ 25 = 32 ✓

Reading both columns gives every factor: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800. The factor calculator does this automatically for any number.

Numbers mathematically connected to 800.

Frequently asked questions about 800

What are the factors of 800?

The factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, and 800. That is 18 factors in total, counting both 1 and 800.

Is 800 a prime number?

No, 800 is not prime — it is a composite number with 18 factors. A prime number has exactly two factors, but 800 is also divisible by 2.

What is the prime factorization of 800?

The prime factorization of 800 is 2⁵ × 5². Written out in full: 2 × 2 × 2 × 2 × 2 × 5 × 5 = 800. Its distinct prime factors are 2, 5.

What two numbers multiply to give 800?

There are 9 pairs of whole numbers that multiply to 800: 1 × 800, 2 × 400, 4 × 200, 5 × 160, 8 × 100, 10 × 80, 16 × 50, 20 × 40, 25 × 32.

What is the sum of the factors of 800?

Adding all the factors of 800 together gives 1953. Excluding 800 itself, the proper factors sum to 1153.

Is 800 a perfect square?

No, 800 is not a perfect square. There is no whole number that multiplies by itself to give 800. The nearest perfect squares are 784 and 841.

What is the largest factor of 800 other than itself?

The largest factor of 800 apart from 800 itself is 400, since 800 ÷ 400 = 2.

How many factors does 800 have?

800 has 18 factors: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, and 800. You can verify this from the prime factorization 2⁵ × 5²: add 1 to each exponent and multiply, giving 6 × 3 = 18.

Explore more

Try another number in the factor calculator, break 800 down further with the prime factorization calculator, or compare 800 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.